1. Field of the Invention
The present invention relates generally to the field of hyperspectral remote sensing applications. More specifically, the present invention relates to real time implementable endmember extraction algorithms.
2. Description of the Related Art
The two major classes of criteria to design endmember extraction algorithms are maximum/minimum simplex volume, such as N-FINDR [1], and maximum/minimum orthogonal projection, such as pixel purity index (PPI) [2]. Pixel Purity Index (PPI) and N-finder algorithm (N-FINDR) have been widely used in hyperspectal imaging, but only PPI is available in the most commonly used remote sensing software, called ENvironment for Visualizing Images (ENVI) commercialized by the Analytical Imaging and Geophysics (AIG) (Research Systems Inc., 2001). The reason for this is that the N-FINDR suffers from five serious drawbacks: 1) computational complexity; 2) inconsistent final results due to its use of random initial conditions; 3) requirement of prior knowledge about the number of endmembers for the N-FINDR to generate; 4) use of dimensionality reduction as a pre-processing and 5) lack of ability in real-time processing.
Although N-FINDR has become one of standard techniques in endmember extraction, its computational complexity makes it extremely expensive to use because it must conduct an exhaustive search for endmembers simultaneously. If there are N data samples and it is required to find p endmembers from these N samples, one would need to exhaust
      (                            N                                      p                      )    =                    N        !                              p          !                ⁢                              (                          N              -              p                        )                    !                      ⁢                  ⁢    p    ⁢          -        ⁢          combinations      ⁢                          .      In addition, in using random initial conditions, the N-FINDR produces different results if a different set of random initial conditions is used. Furthermore, using N-FINDR also requires knowing the number of endmembers to be generated. Most importantly, it nearly impossible to implement N-FONDR in real-time due to above-mentioned drawbacks, computational complexity, use of random initial conditions and necessity of performing dimensionality reduction as a pre-processing step.
There is a recognized need in the art in real world applications for improved methods for endmember extraction from hyperspectral images that mitigate the problems in N-FINDR. Specifically, the prior art is deficient in the lack of improved sequential, real time implementable versions of N-FINDR algorithms based on the maximum simplex volume criterion. The present invention fulfills this long-standing need and desire in the art.